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In a triangle FGH, FK is perpendicular to GH and \( \angle G = \angle H\). By which congruency criteria \( \Delta FKG \cong \Delta FKH\)?
As we can write FG = FH. Therefore, the triangles are congruent by the A.S.A. criteria of congruency.
In a triangle MNP, MT is perpendicular to NP and MN = MP. By which congruency criteria \( \Delta MTN \cong \Delta MTP\)?
(1)
Therefore the triangles are congruent by the R.H.S. criteria of congruency.
Which of the following statement is correct?
Two equilateral triangles having same length are always congruent. If two right triangles do not have same hypotenuse then they can’t be congruent. Rhombus and square are not congruent because the angles of rhombus are not 90°.
In a triangle JKL, \( \angle K = 90^{\circ} \). Which of the following statement is correct?
The side opposite to the right angle is the longest in a right triangle. Therefore, JL is the longest side of the triangle JKL.
Which of the following lengths will not form a triangle?
The triangle only forms when sum of lengths of two sides is greater than the length of the third side. The triangle will not form in the option 4.7 cm, 6.3 cm, 11.4 cm because 4.7 + 6.3 = 11 which is less than 11.4.
If \( \Delta MNP \cong \Delta RST\) by the S.A.S criteria of congruency then which of the following is correct?
The triangles are congruent by S.A.S. so two pairs of side should be equal and the angles between them are also equal to each other. Therefore, .
In \( \Delta PQR \), PQ = 10 cm, QR = 12 cm and PR = 14 cm. Identify the correct relation among the angles of the triangle PQR.
The angle opposite to the longest side is the greatest. Therefore, .
If \( \Delta PQR \cong \Delta TUV \) then which of the following is correct?
When two triangles are congruent then the corresponding angles are equal. Therefore, .
In \( \Delta PQR \), PQ > QR. Identify the correct relation among the angles of the triangle PQR.
The angle opposite to the longer side is greater. As PQ > QR therefore, .
The length of the largest side of a triangle is 14 cm. What are the possible values of the other two sides?
The sum of lengths of two sides must be greater than the length of the third side. 7.8 + 6.3 = 14.1 which is greater than 14. Therefore, possible lengths of other two sides are 7.8 cm and 6.3 cm.
If \( \Delta ABC \cong \Delta MNP \) by the S.S.S. criteria of congruency then which of the following is correct?
The triangles ABC and MNP are congruent by the S.S.S. criteria of congruency therefore the lengths of the corresponding sides must be equal. Therefore the correct option is AB = MN, BC = NP and AC = MP.
\( \Delta JKL \cong \Delta MNP \) and \( \angle J = 30^{\circ} and \angle L = 85^{\circ}\) and the length of MP is 6.3 cm. Which of the following is correct?
(1)
The length corresponding to MP is JL, therefore, JL = 6.3 cm.
JKLM is a quadrilateral in which JK = LK and JM = LM. What is the measure of angle KLM?
Draw the diagonal KM and the JKM will be congruent to the triangle LKM because JK = LK, JM = LM and KM is the common side. There the angle MKL will be 53° and the angle KML will be 23°.
(1)
In the following figure FK = HK = KG. What is the measure of angle FGH?
Angles opposite to equal sides are equal. Therefore,
(1)